Cable is a general term for wires and electric lines that connecting electrical components, electrical equipments or control devices in electromechanical system of complex product, and plays important role as a medium for transferring power and signal. The rationality of layout design and the assembly reliability of cable will directly affect the performance of the final product. In recent years, with the development of CAD technology and virtual reality technology, assembly simulation of a flexible cable under virtual environment has gradually attracted attention. Through the assembly simulation of the cable, the assemblability and rationality of cable design can be verified, and can thus forecast the problems that may occurred in the practical assembling of the cable, so as to solve the problems in advance.
Model representation of the cable is the basis for the assembly simulation of the cable under virtual environment. The model representation of the cable under virtual environment needs, in one hand, to truly represent a spatial shape and a physical property of the cable, and in the other hand, also to meet the real-time requirement of a virtual reality system, that is, the solving rate shall meet the operational requirement of the virtual assembly simulation.
The geometry model of the cable may lacks of reality if the physical property of the cable is not taken into account. A physical model of the cable becomes the major research project of domestic and overseas scholars in recent years, because the physical model can more truly reflect the shape of the cable. A spring-mass model is used as a simple, good real-time physical model in simulating a flexible body such as fabric, skin, cable etc. The spring-mass model is initially proposed by Haumann and Parent (The behavioral test-bed: Obtaining complex behavior from simple rules, The Visual Computer, 1988, 4(6): 332-347); they assemble an experimental apparatus by connecting mass points with springs. According to the theory of Newton's laws of motion, the mass points will be moved under external force.
Provot et al. (Deformation constraints in a mass-spring model to describe rigid cloth behavior, Proceedings of the 1995 Graphics Interface Conference, Canadian Information Processing Soc., Quebec, Que, Can, 1995, pp. 147-154) improve the spring-mass model by adding a linear spring, which is also referred to as bending spring, in between two spaced mass points, which resulting in good effect in terms of simulating the bending behavior of fabric. Loock et al. (A virtual environment for interactive assembly simulation: from rigid bodies to deformable cables, 5th World Multiconference on Systemics, Cybernetics and Informatics (SCI), Citeseer, 2001, pp. 325-332) use the spring-mass model in modeling of the flexible cable, and improve the spring-mass model once again. They abstract the cable into being consisted of mass points and springs, wherein two adjacent mass points are still connected by a linear spring, but a coil spring, instead of the linear spring between two spaced mass points, is added at each of the mass points, thereby improving bending effect of the cable. The improved model is used to stimulate spatial shapes of cables of different rigidities under gravity.
On the basis of the above mentioned model, Wang Zhibin et al. (A multi-branch mass-spring model for virtual assembly of cable harness, Journal of Mechanical Engineering, 2014, Vol 50, No. 3, pp. 174-183) propose a multi-branch spring-mass model for modeling of a multi-branch cable by adding branch points, which realize the simulation of the multi-branch cable. Although their model is capable of modeling tension, bending, gravity and other factors of the cable, the torsion of cable is not taken into account, so that their model cannot truly represent the spatial shape of the cable. Moll et al. (Path planning for deformable linear objects, IEEE Transactions on Robotics, 2006, 22(4): 625-636) describe equilibrium postures of a one-dimensional deformable body such as a cable etc. under a variety of operational constraints using an energy curve model. They associate energy of a curve with its curvature and torsion, and consider the curve to be in an equilibrium state when having minimum energy under a variety of constraints. But they assume that the curve has no mass and tension, so consider straight segment without distortion as having minimum energy in the absence of external force.
Hergenröther et al. (Real-time virtual cables based on kinematic simulation, Proceedings of WSCG, Univ. of West Bohemia, Plzen, Czech Republic, 2000, pp. 402-409) regard the cable as a series of cylindrical segments of equal length connected by spherical nodes for a fixed-length cable, arrange a coil spring at each of the nodes to represent bending of the cable, and solve the model using a method of energy (which is the sum of potential energy of the cylindrical segments and elastic potential energy of the coil springs) minimization and step-by-step subdivision, but torsion of the cable is still not represented. Wei Fayuan et al. model the cable with an inverse kinematics model by regarding the cable as a snake-like robot having multiple joints, and simulate the installation of the cable using an inverse kinematics method in robot theory. However, they assume that turning angles are the same at each joint in solving the model, which cannot accurately simulate the actual shape of the cable.
Liu Jianhua et al. (Motional cable harness physical characteristic oriented modeling and kinetic simulation technology in virtual environment, Journal of Mechanical Engineering, 2011, 47(9): 117-124) propose a method of physical property modeling and motion simulation for a movable cable based on a Kirchhoff thin elastic rod mechanical model. Grégoire et al. (Interactive simulation of one-dimensional flexible parts, Computer-Aided Design, 2007, 39(8): 694-707) represent the shape of cable with a general spring-mass model, and represent bending and torsion of the cable with a Cosserat model, and solve the equilibrium state of the cable by energy minimization process. These two methods can more truly represent the shape of the cable with higher accuracy, however, the solution process is complicated, and it is difficult to meet real-time requirement in interactive assembly.
In addition, the modeling of a one-dimension flexible body such as surgical suture and rope in other fields can be a reference for cable modeling. Since the suture, rope and the like often needed to be knotted in practical application, a knotting model of which puts forward higher requirement for real-time performance, collision detection and response and other aspects, which requirement is similar to that in the interactive assembly simulation for the modeling of the cable.
When modeling a rope, Brown et al. (Real-time knot-tying simulation, Visual Computer, 2004, 20(2-3): 165-179) regard the rope as a series of rigid straight segments of equal length connected by spherical nodes, and each of the nodes has two rotational degrees of freedom. Further, in order to meet real-time requirement in knotting the rope, they focus on treating the contact of the rope with surrounding objects and with itself, and solve the model using a simple “Follow the Leader” method, so that the nodes are moved along with the dragged points without changing the length of each of the rigid segments, which resulting in better knotting effect.
With respect to the problem in training laparoscopic operation, Wang et al. (Knot-tying with visual and force feedback for VR laparoscopic training, Proceedings of the 27th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE-EMBS), 2005) perform a study on surgical suture simulation, and they synthetically take a variety of physical factors into account in developing a knotting model based on springs and mass points, thereby achieving the simulation of a knotted suture with force feedback. The knotting model differs from the cable model in that, the former places more focus on processing collision of a one-dimensional flexible body and has lower requirement in reality of its shape, but the cable model has higher requirement in reality.
From the foregoing, only the gravity, tensile and bending properties of the cable are taken into account in the conventional spring-mass model of the cable, but the torsion property of the cable is not taken into account, and the torsion effect of the cable cannot be modeled. Therefore, the simulation effect is not realistic enough, the rate of model solution is slow and the real-time requirement in the interactive assembly simulation cannot be met, so that the reliability in the process of assembling the flexible cable in the prior art cannot be ensured.